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In this circuit, we are asked to analyze the current through \( R_2 \) when capacitor \( C_2 \) is fully charged. Let's go through the reasoning step-by-step.

1. **Capacitor Behavior**: When a capacitor is fully charged, it behaves like an open circuit because no further current can flow through it. Hence, once \( C_2 \) is fully charged, the branch containing \( R_2 \) and \( C_2 \) will have no current flowing through it.

2. **Current through \( R_2 \)**: Since \( C_2 \) is fully charged, no current will flow through the \( R_2 \) branch, making the current through \( R_2 \) zero.

Thus, the correct answer to the question is:
- **The current is zero**.

Would you like further clarification or details? Here are some related questions to deepen your understanding:

1. How does the charging time of a capacitor depend on its capacitance and resistance?
2. What happens to the total current \( I_0 \) in the circuit once \( C_2 \) is fully charged?
3. How can we determine the voltage across \( R_1 \) after \( C_2 \) is fully charged?
4. What is the role of \( C_1 \) in this circuit configuration?
5. What changes occur in the circuit if \( C_2 \) were replaced with a resistor?

**Tip**: When analyzing circuits with capacitors, remember that capacitors block DC current after becoming fully charged, which can simplify the analysis.

In the circuit below, assume the total current out of the battery is I₀. If the capacitor C₂ is fully charged, what is the current through R₂?

Understand how to determine the current through resistor R₂ in a circuit where the capacitor C₂ is fully charged. This problem covers key concepts in electric circuits, including Ohm's Law, capacitor behavior, and Kirchhoff's Laws. Ideal for high school students in Grades 10-12.

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